PXD10 Datasheet, PDF (98/130 Pages) Lumins Inc. – 4” Dia.X 6” extruded aluminum step poles

Electrical characteristics
(since the time constant in reality would be faster) in which C_P2 is reported in parallel to C_P1 (call
C_P = C_P1 + C_P2), the two capacitances C_P and C_S are in series, and the time constant is
₁
=
RSW
+
RAD

-C----P-----^----C----S--
CP + CS
Eqn. 8
Equation 8 can again be simplified considering only C_S as an additional worst condition. In reality,
the transient is faster, but the A/D converter circuitry has been designed to be robust also in the
very worst case: the sampling time T_S is always much longer than the internal time constant:
₁  RSW + RAD  CS « TS
Eqn. 9
The charge of C_P1 and C_P2 is redistributed also on C_S, determining a new value of the voltage V_A1
on the capacitance according to Equation 10:
VA1  CS + CP1 + CP2 = VA  CP1 + CP2
Eqn. 10
• A second charge transfer involves also C_F (that is typically bigger than the on-chip capacitance)
through the resistance R_L: again considering the worst case in which C_P2 and C_S were in parallel
to C_P1 (since the time constant in reality would be faster), the time constant is:
₂  RL  CS + CP1 + CP2
Eqn. 11
In this case, the time constant depends on the external circuit: in particular imposing that the
transient is completed well before the end of sampling time T_S, a constraints on R_L sizing is
obtained:
10  ₂ = 10  RL  CS + CP1 + CP2  TS
Eqn. 12
Of course, R_L shall be sized also according to the current limitation constraints, in combination
with R_S (source impedance) and R_F (filter resistance). Being C_F definitively bigger than C_P1, C_P2
and C_S, then the final voltage V_A2 (at the end of the charge transfer transient) will be much higher
than V_A1. Equation 13 must be respected (charge balance assuming now C_S already charged at
V_A1):
VA2  CS + CP1 + CP2 + CF = VA CF + VA1 CP1 + CP2 + CS
Eqn. 13
The two transients above are not influenced by the voltage source that, due to the presence of the R_FC_F
filter, is not able to provide the extra charge to compensate the voltage drop on C_S with respect to the ideal
PXD10 Microcontroller Data Sheet, Rev. 1
98
Freescale Semiconductor